Graphene-based optical modulators
© Luo et al.; licensee Springer. 2015
Received: 21 January 2015
Accepted: 17 March 2015
Published: 25 April 2015
Optical modulators (OMs) are a key device in modern optical systems. Due to its unique optical properties, graphene has been recently utilized in the fabrication of optical modulators, which promise high performance such as broadband response, high modulation speed, and high modulation depth. In this paper, the latest experimental and theoretical demonstrations of graphene optical modulators (GOMs) with different structures and functions are reviewed. Particularly, the principles of electro-optical and all-optical modulators are illustrated. Additionally, the limitation of GOMs and possible methods to improve performance and practicability are discussed. At last, graphene terahertz modulators (GTMs) are introduced.
KeywordsGraphene Optical modulator Photonics Absorption Electro-absorption All-optical Terahertz Broadband Ultrafast
As one of the key components in photonics systems, an optical modulator is a device used to control the fundamental characteristics of a carrier light propagating in free space or in an optical waveguide upon an external electronics/photonics signal . In order to meet specific requirements in applications, such as modern lasers, optical communication, and terahertz communication, various designs have been demonstrated. And thanks to the latest development in nanotechnology and material science, advanced-function materials are progressively involved in device fabrication. For instance, group III-V materials , germanium [3,4], polymers [5,6], and graphene [7,8] have been applied and incorporated to silicon-based modulators to form hybrid devices, with the aim to improve the modulation speed, broaden the modulation range, and reduce the device footprint and energy consumption. According to the parameters being modulated, these devices can be categorized as amplitude, phase, or polarization modulators. Generally, amplitude modulation is the most common due to its classified system. And the performance can be characterized by optical bandwidth, modulation depth, modulation speed, insertion loss, area efficiency (footprint), and power consumption .
As the prime material for the semiconductor industry, silicon modulators have to be fabricated in large scale to obtain enough modulation depth, due to a relatively weak high-order electro-optical effect. On the other hand, modulators based on germanium and other compounds have problems to be integrated with current complementary metal-oxide-semiconductor (CMOS) techniques. For modulators with resonators, narrow modulation bandwidth limits their development. By contrast, graphene can cover the needs of scale, speed, and techniques. And integration with graphene can help current modulators to improve their performance.
Graphene, a single layer of hexagonally packed carbon atoms, was first isolated from graphite via mechanical exfoliation in 2004. For these highly confined two-dimensional crystals, in-plane carbon atoms are connected by strong σ-bonds, while adjacent layers only share weak van de Waals force. The unique crystalline structure endows graphene extraordinary electronic, optical, thermal, and mechanical properties. Graphene is expected to grow into the new silicon in future electronics and photonics. Many proof-of-concept photonics devices based on graphene, including photodetectors [10,11], ultrafast lasers [12,13], polarization controllers , and plasmonic structures [15-17], have been demonstrated.
In this review article, we provide a brief overview of graphene-based optical modulators. Our survey is not intended to cover every single device reported in prior publication, but rather to introduce some typical designs and highlight some recent notable work. Classified by whether electrical elements are involved or not, the principle and paradigms of electro-optical and all-optical graphene optical modulators are elaborated in the ‘Electro-optical graphene optical modulator’ and ‘All-optical grapheme optical modulator’ sections, respectively. In addition, graphene-based material systems for THz wave modulation are discussed in the ‘Graphene terahertz modulator’ section. The article closes with a final conclusion and outlook in the ‘Conclusions’ section.
Electro-optical graphene optical modulator
Mechanism of electro-absorption
Due to the sp2 hybridization of carbon atoms, graphene has a unique electronic structure in that the conduction band and valence band meet at Dirac points like two cones [10,11]. A linear energy-momentum dispersion relation can be noted in the vicinity of Dirac points and carries behavior that can be modeled as massless Dirac fermions.
Both interband transition and intraband transition are related to chemical potential μ and the frequency of incident light ω. When μ = 0, no intraband transition will happen. When |μ| < ħ ω/2, (slightly n-doped or p-doped) optical transition is dominated by interband transition. In n- and p-doped (corresponding to positive and negative gating voltage) graphene, the incident photons with energy less than 2E F cannot be absorbed. This is because the electron states in the conduction band are filled up as shown in Figure 2b or there are no electrons in the valence band available for interband transition as shown in Figure 2c. Thus, if the incident light is fixed, by electrically tuning the Fermi level, interband transitions can be turned on and off [21,22]. When |μ| < ħ ω/2, the intraband transition related to the terahertz range will be dominant [23-25]. At this condition, plasmon momentum enhancement is allowed and propagation of surface plasmon in graphene becomes possible [26-28].
In earlier theory demonstrations, graphene was treated as an isotropic material [29,30]. Graphene can transfer from dielectric-like to metallic-like when the permittivity is tuned to approach zero. Recently, graphene became well accepted as an anisotropic material. When graphene was treated as an anisotropic material [31,32], a linear relation between its in-plane permittivity and effective mode index can be observed. The electric distributions are also different in or out of graphene when it is treated as an isotropic or anisotropic material . In this case, the in-plane permittivity can be tuned by the chemical potential, while the out-of-plane permittivity (in a direction perpendicular to the graphene sheet) does not .
Basic designs of electro-optical graphene optical modulator (GOM)
Advanced structures for electro-optical GOM
Integration of graphene with other optical modulators
In addition, a device integrating both GOMs and a graphene optical photodetector was experimentally demonstrated . Recently, Zhou et al. first theoretically found a quasilinear relation between the phase change and chemical potential of graphene, which implied an optical phase modulator .
RC constant limit in electro-optical GOM
In theory, the high carrier mobility of graphene will lead to an ultrahigh modulation speed. However, in experimental demonstration, the modulation speed is still limited at approximately 1 GHz [7,8] lower  in electro-optical GOMs. The reason is the ‘electrical bottleneck’ - RC constant. The electronic circuit of this device can be equivalent to RC low-pass filter (LPF). The 3 dB cut-off frequency of electronic signal can be calculated by f = 1/2πRC, where R is the total cascade resistance and C is the total capacitance between counter electrodes. These factors can be measured by a network analyzer. The all-optical method is an efficient way to avoid this bottleneck.
All-optical graphene optical modulator
The future optical fiber communication system requires a modulator whose operation speed is larger than 100 Ghz . Although the graphene-based modulator has the potential to obtain a modulation rate of 500 GHz, the practical electro-absorption modulator based on graphene is limited to approximately 1 GHz due to the RC constant [7,8]. A direct method to avoid this ‘electrical bottleneck’ is to make the modulator all-optical. That is, light modulates light. The all-optical graphene optical modulators demonstrated at present are based on saturable absorption in graphene.
Mechanism of saturable absorption
Saturable absorption is a property of materials where the absorption of light is decreased to a steady level at sufficiently high incident light intensity . This optical nonlinearity is widely applied to generate short laser pulses as optical absorber in mode-locked lasers [20,47]. It is worth noting that high incident optical intensity may damage the material during absorption. Although many semiconductors such as GaAs also show saturable absorption, only those whose saturable intensity is much lower than the optical damage threshold can be used in practical devices . Optical devices based on graphene with high optical damage threshold have been fabricated . Moreover, in saturable absorption devices, compared with single-walled carbon nanotubes (SWNTs)  or semiconductor saturable absorber mirrors (SESAMs) , graphene is much easier to be fabricated without band gap engineering or chirality (diameter) control.
Basic designs of all-optical GOM
Liu et al. firstly experimentally showed all-optical modulation using a graphene-covered microfiber, which is compatible with the optical fiber system . A chemical vapor deposition (CVD)-synthesized graphene film is dry transferred by polydimethylsiloxane (PDMS) to cover the microfiber on MgF2 substrate, as is shown in Figure 7a. In the substrate-supported structure, the substrate should have a low refractive index to guarantee the total reflection. Pump light (1,060 nm) and carrier (signal) light (1,550 nm) together transmit through the microfiber and the intensity of carrier light varied with pump light, as is shown in Figure 7b,c,d. In this work, a modulation speed of only 1 MHz is achieved due to the low switching frequency of pump light. A modulation depth of approximately 5 dB is achieved by single-layer graphene. And as is expected, a higher modulation depth of approximately 13 dB is achieved by double-layer graphene.
Advanced structures for all-optical GOM
Theoretically, if the intensity of pump light is strong enough (lower than the optical damage threshold), graphene can be totally transparent to carrier light. Thus, the maximum modulation depth is determined by the optical absorption when the pump light is off, which is largely related to the interaction length and position of the graphene sheet. However, in the works above, sufficiently saturable absorption is not achieved and absorption of carrier light is gradually varied with the changes of pump intensity as shown in the inset of Figure 8e . In the aspect of transmission property, graphene integrated with a microfiber has higher absorption along with increasing wavelength, which can be explained by higher evanescent field for longer wavelength at the graphene interface . In addition, different polarization of the pump light can result in approximately 1 dB change of modulation depth .
Graphene terahertz modulator (GTM)
In the past decades, terahertz (THz) technology was found to be applied in diverse areas such as astronomy, biology/medicine , communications , and defense . Although numerous advances have been achieved, most of them focus on emitters and detectors. Devices like active filters and modulators which can be integrated with current solid-state continuous-wave (CW) terahertz sources and detectors such as quantum cascade lasers , resonant tunneling diode oscillators , Schottky diodes , backward diodes , or future graphene-based terahertz devices  still need to be improved . As a gapless semiconductor, graphene is a natural material for long-wave applications such as THz. With the advantages mentioned in the introduction, graphene shows great potential in modulators and detectors .
The optical conductivity of graphene is determined by interband transition and intraband transition, respectively, mainly for short wavelength (infrared and visible) and long wavelength (terahertz) [23-25]. Thus, electrostatically tuning the density of states (DOS) available for intraband transitions provides the possibility to effectively control the terahertz absorption [69,70]. As a result, large gating voltage is usually used. A high modulation depth of >90% has been shown by employing graphene in place of a metal gate in an AlGaAs/GaAs two-dimensional electron-gas (2DEG) terahertz modulator, which provides a modulation of <30 only .
Following Sensale-Rodriguez et al.’s first demonstration of GTM , Weis et al. fabricated an all-optical GTM in the same year, 2012 . They deposited graphene on silicon (GOS) to enhance the absorption as shown in Figure 9b. Upon infrared photodoping, a broadband modulation from 0.2 to 2 THz was achieved. Moreover, the modulator showed a maximum modulation depth of 99%.
GTM with resonators
Due to accurate and deep modulation in the THz range, integration with resonators shows a way to cover special needs [75-77]. In graphene-integrated modulators, the resonators not only enhance the interaction between graphene and terahertz wave but also bring the advantage to decrease the bias . Degl’Innocenti et al. recently integrated metallic split-ring resonators (SRRs) and single-layer graphene on one substrate . A modulation depth of 18% and a bandwidth from 2.2 to 3.1 THz were achieved. Additionally, the structure, as is shown in Figure 9c, showed a low bias of 0.5 V . Recently, using resonators, terahertz modulators based on metamaterial and graphene have also been studied . However, complex design and fabrication increase the difficulty and cost.
Optical modulators are an important device to the current and future optical systems and still need to be improved. Graphene shows great potential in fabricating broadband and ultrafast optical modulators. Optical transition including interband and intraband transitions in graphene is the main process during absorption. Electro-optical GOMs have been demonstrated while the modulation speed is limited to approximately 1 GHz due to the RC constant. The position of the graphene sheet efficiently influences the light-graphene interaction. Higher modulation depth can be easily achieved by placing graphene close to the maximum of the electric field. Following the first demonstration, many optical modulators enhanced by graphene have been theoretically and experimentally demonstrated. However, higher modulation speed is necessary for current electro-optical GOMs. Driven by saturable absorption, all-optical GOMs show a potential of ultrafast modulation speed due to the ultrafast relaxation time. But direct measurement of ultrafast modulation has not been demonstrated. In the field of terahertz, graphene has a prominent advantage of high modulation depth. Electro-optical and all-optical modulation are both possible. In principle, theoretical simulations go much further than experiment. GOMs with new structures and high performance tend to be demonstrated in the near future.
This work was supported by the National Basic Research Program of China (973 Program, Grant No. 2013CB933301) and National Natural Science Foundation of China (Grant Nos. 51272038 and 51302030).
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